Vasconcelos' SCM conjecture for height-three homogeneous ideals

Let $S$ be a polynomial ring and let $I$ be a homogeneous ideal of height $3$. Write $\mu(I)$ for the minimum number of generators, let $g=\operatorname{ht}(I)$, and define the deviation of $I$ to be $\mu(I)-g$. Say that $I$ is generically a complete intersection, that $I$ is Gorenstein, and that the resolution of $S/I$ is pure. Finally, $I$ is strongly Cohen--Macaulay (SCM) when all its Koszul homology modules are Cohen--Macaulay.

Vasconcelos' SCM conjecture. If $I$ has deviation at least $3$, is generically a complete intersection, is not Gorenstein, and the resolution of $S/I$ is pure, then $I$ is not SCM.

The text says that numerical computations and cited results support this conjecture and explicitly states that it is still open.